Regression Tables

betaO0 : intercept in outcome equation

Main Effects 2nd Order Effects Interaction Effects Both Effects
DV : Absolute Error of betaO0, sample trimmed off 0.3%
OLS Heckit Copula OLS Heckit Copula OLS Heckit Copula OLS Heckit Copula
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept) 0.392*** 0.432*** 0.259*** 0.427*** 0.411*** 0.257*** 0.391*** 0.431*** 0.259*** 0.427*** 0.410*** 0.257***
(0.005) (0.006) (0.002) (0.006) (0.006) (0.003) (0.005) (0.006) (0.002) (0.006) (0.006) (0.003)
dependence 0.906*** 0.159*** −0.003 0.342*** −0.003 0.007 0.910*** 0.160*** −0.003 0.338*** −0.004 0.007
(0.006) (0.006) (0.002) (0.021) (0.022) (0.009) (0.005) (0.006) (0.002) (0.020) (0.022) (0.009)
dependence^2 0.701*** 0.202*** −0.013 0.711*** 0.205*** −0.013
(0.025) (0.026) (0.011) (0.024) (0.026) (0.011)
selectivity −0.161*** −0.143*** −0.045*** −0.161*** −0.143*** −0.045*** −0.013*** −0.096*** −0.052*** −0.013*** −0.096*** −0.052***
(0.002) (0.002) (0.001) (0.002) (0.002) (0.001) (0.003) (0.004) (0.001) (0.003) (0.004) (0.001)
selectivity^2 0.020*** 0.052*** 0.002 0.021*** 0.053*** 0.002
(0.004) (0.004) (0.002) (0.003) (0.004) (0.002)
dependence*selectivity −0.397*** −0.124*** 0.018*** −0.399*** −0.125*** 0.018***
(0.007) (0.007) (0.003) (0.007) (0.007) (0.003)
X1 ~ normal - - - - - - - - - - - -
X1 ~ uniform −0.031*** −0.023*** −0.007*** −0.031*** −0.023*** −0.007*** −0.031*** −0.023*** −0.007*** −0.031*** −0.023*** −0.007***
(0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002)
X1 ~ poisson 0.101*** 0.157*** 0.039*** 0.102*** 0.157*** 0.039*** 0.104*** 0.157*** 0.039*** 0.104*** 0.158*** 0.039***
(0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002)
X1 ~ normal mixture −0.010* 0.051*** 0.012*** −0.010* 0.051*** 0.012*** −0.010* 0.051*** 0.012*** −0.010* 0.051*** 0.012***
(0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002)
selection ~ logit - - - - - - - - - - - -
selection ~ probit −0.068*** −0.059*** −0.018*** −0.068*** −0.059*** −0.018*** −0.068*** −0.059*** −0.018*** −0.068*** −0.059*** −0.018***
(0.003) (0.004) (0.001) (0.003) (0.004) (0.001) (0.003) (0.004) (0.001) (0.003) (0.004) (0.001)
outcome ~ logit - - - - - - - - - - - -
outcome ~ normal −0.423*** −0.370*** −0.146*** −0.423*** −0.370*** −0.146*** −0.424*** −0.370*** −0.146*** −0.424*** −0.370*** −0.146***
(0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002)
outcome ~ poisson −0.616*** −0.456*** −0.222*** −0.617*** −0.456*** −0.222*** −0.617*** −0.456*** −0.222*** −0.618*** −0.456*** −0.222***
(0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002)
outcome ~ probit −0.222*** −0.118*** −0.046*** −0.222*** −0.118*** −0.046*** −0.221*** −0.118*** −0.046*** −0.221*** −0.118*** −0.046***
(0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002) (0.005) (0.005) (0.002)
Num.Obs. 38198 38202 38302 38198 38202 38302 38198 38202 38302 38198 38202 38302
R2 0.568 0.304 0.316 0.577 0.308 0.316 0.605 0.309 0.316 0.614 0.314 0.316
R2 Adj. 0.568 0.304 0.315 0.577 0.308 0.316 0.605 0.309 0.316 0.614 0.313 0.316
AIC 24675.5 29142.0 −41221.9 23858.5 28902.9 −41220.8 21249.5 28857.4 −41259.5 20326.0 28612.2 −41258.4
BIC 24769.6 29236.0 −41127.8 23969.7 29014.0 −41109.6 21352.2 28960.0 −41156.8 20445.7 28732.0 −41138.7
Log.Lik. −12326.756 −14559.978 20621.926 −11916.268 −14438.443 20623.395 −10612.775 −14416.704 20641.745 −10148.980 −14292.123 20643.215
RMSE 0.33 0.35 0.14 0.33 0.35 0.14 0.32 0.35 0.14 0.32 0.35 0.14

betaO1 : coefficient on endogenous variable X1

Main Effects 2nd Order Effects Interaction Effects Both Effects
DV : Absolute Error of betaO1, sample trimmed off 0.3%
OLS Heckit Copula OLS Heckit Copula OLS Heckit Copula OLS Heckit Copula
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept) 0.182*** 0.267*** 0.168*** 0.181*** 0.274*** 0.165*** 0.181*** 0.267*** 0.168*** 0.180*** 0.273*** 0.165***
(0.002) (0.004) (0.002) (0.003) (0.005) (0.002) (0.002) (0.004) (0.002) (0.003) (0.005) (0.002)
dependence 0.139*** 0.210*** 0.001 0.043*** −0.074*** 0.004 0.139*** 0.211*** 0.001 0.042*** −0.075*** 0.004
(0.002) (0.005) (0.002) (0.009) (0.017) (0.006) (0.002) (0.005) (0.002) (0.009) (0.017) (0.006)
dependence^2 0.119*** 0.352*** −0.004 0.120*** 0.355*** −0.004
(0.011) (0.020) (0.007) (0.011) (0.020) (0.007)
selectivity −0.046*** −0.080*** −0.021*** −0.046*** −0.080*** −0.021*** −0.027*** −0.031*** −0.019*** −0.027*** −0.031*** −0.019***
(0.001) (0.002) (0.001) (0.001) (0.002) (0.001) (0.001) (0.003) (0.001) (0.001) (0.003) (0.001)
selectivity^2 0.014*** 0.027*** 0.004*** 0.014*** 0.027*** 0.004***
(0.002) (0.003) (0.001) (0.002) (0.003) (0.001)
dependence*selectivity −0.052*** −0.131*** −0.006** −0.053*** −0.132*** −0.006**
(0.003) (0.006) (0.002) (0.003) (0.006) (0.002)
X1 ~ normal - - - - - - - - - - - -
X1 ~ uniform 0.037*** 0.027*** 0.035*** 0.037*** 0.027*** 0.035*** 0.037*** 0.027*** 0.035*** 0.037*** 0.027*** 0.035***
(0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001)
X1 ~ poisson 0.024*** 0.052*** 0.011*** 0.024*** 0.052*** 0.011*** 0.024*** 0.053*** 0.011*** 0.024*** 0.053*** 0.011***
(0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001)
X1 ~ normal mixture −0.031*** −0.018*** −0.020*** −0.031*** −0.018*** −0.020*** −0.031*** −0.018*** −0.020*** −0.031*** −0.018*** −0.020***
(0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001)
selection ~ logit - - - - - - - - - - - -
selection ~ probit 0.012*** −0.012*** 0.004*** 0.012*** −0.012*** 0.004*** 0.012*** −0.012*** 0.004*** 0.012*** −0.012*** 0.004***
(0.001) (0.003) (0.001) (0.001) (0.003) (0.001) (0.001) (0.003) (0.001) (0.001) (0.003) (0.001)
outcome ~ logit - - - - - - - - - - - -
outcome ~ normal −0.133*** −0.285*** −0.112*** −0.133*** −0.285*** −0.112*** −0.133*** −0.285*** −0.112*** −0.133*** −0.285*** −0.112***
(0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001)
outcome ~ poisson −0.205*** −0.328*** −0.156*** −0.205*** −0.328*** −0.156*** −0.205*** −0.328*** −0.156*** −0.205*** −0.328*** −0.156***
(0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001)
outcome ~ probit −0.042*** −0.036*** −0.023*** −0.042*** −0.036*** −0.023*** −0.042*** −0.035*** −0.023*** −0.042*** −0.035*** −0.023***
(0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001) (0.002) (0.004) (0.001)
Num.Obs. 38220 38199 38303 38220 38199 38303 38220 38199 38303 38220 38199 38303
R2 0.326 0.284 0.340 0.329 0.291 0.340 0.331 0.294 0.340 0.335 0.302 0.340
R2 Adj. 0.326 0.284 0.339 0.329 0.291 0.340 0.331 0.294 0.340 0.334 0.301 0.340
AIC −39102.2 9563.1 −70842.4 −39298.3 9190.4 −70855.9 −39403.6 9029.9 −70848.2 −39604.4 8644.3 −70861.7
BIC −39008.1 9657.2 −70748.3 −39187.1 9301.6 −70744.7 −39301.0 9132.5 −70745.6 −39484.7 8764.0 −70742.0
Log.Lik. 19562.075 −4770.557 35432.211 19662.140 −4582.208 35440.959 19713.803 −4502.946 35436.103 19816.221 −4308.161 35444.857
RMSE 0.15 0.27 0.10 0.14 0.27 0.10 0.14 0.27 0.10 0.14 0.27 0.10

betaO2 : coefficient on exogenous variable X2

Main Effects 2nd Order Effects Interaction Effects Both Effects
DV : Absolute Error of betaO2, sample trimmed off 0.3%
OLS Heckit Copula OLS Heckit Copula OLS Heckit Copula OLS Heckit Copula
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept) 0.217*** 0.228*** 0.160*** 0.223*** 0.243*** 0.157*** 0.217*** 0.228*** 0.160*** 0.223*** 0.243*** 0.157***
(0.003) (0.004) (0.001) (0.003) (0.004) (0.002) (0.003) (0.004) (0.001) (0.003) (0.004) (0.002)
dependence 0.124*** 0.217*** 0.007*** −0.029** −0.088*** 0.010+ 0.125*** 0.218*** 0.007*** −0.029** −0.089*** 0.010+
(0.003) (0.004) (0.001) (0.010) (0.014) (0.005) (0.003) (0.004) (0.001) (0.010) (0.014) (0.005)
dependence^2 0.190*** 0.380*** −0.004 0.191*** 0.382*** −0.004
(0.012) (0.017) (0.006) (0.012) (0.017) (0.006)
selectivity −0.045*** −0.064*** −0.019*** −0.045*** −0.064*** −0.019*** −0.025*** −0.021*** −0.019*** −0.025*** −0.021*** −0.019***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.002) (0.002) (0.001) (0.002) (0.002) (0.001)
selectivity^2 0.011*** 0.017*** 0.004*** 0.011*** 0.018*** 0.004***
(0.002) (0.002) (0.001) (0.002) (0.002) (0.001)
dependence*selectivity −0.054*** −0.116*** −0.001 −0.055*** −0.117*** −0.001
(0.003) (0.005) (0.002) (0.003) (0.005) (0.002)
X1 ~ normal - - - - - - - - - - - -
X1 ~ uniform −0.012*** −0.013*** −0.002* −0.012*** −0.013*** −0.002* −0.012*** −0.013*** −0.002* −0.012*** −0.013*** −0.002*
(0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001)
X1 ~ poisson 0.023*** 0.034*** 0.010*** 0.023*** 0.034*** 0.010*** 0.023*** 0.034*** 0.010*** 0.024*** 0.034*** 0.010***
(0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001)
X1 ~ normal mixture −0.003 0.001 0.008*** −0.003 0.001 0.008*** −0.003 0.001 0.008*** −0.003 0.001 0.008***
(0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001)
selection ~ logit - - - - - - - - - - - -
selection ~ probit −0.009*** −0.010*** 0.003** −0.009*** −0.010*** 0.003** −0.009*** −0.009*** 0.003** −0.009*** −0.009*** 0.003**
(0.002) (0.002) (0.001) (0.002) (0.002) (0.001) (0.002) (0.002) (0.001) (0.002) (0.002) (0.001)
outcome ~ logit - - - - - - - - - - - -
outcome ~ normal −0.208*** −0.257*** −0.115*** −0.208*** −0.257*** −0.115*** −0.208*** −0.257*** −0.115*** −0.208*** −0.257*** −0.115***
(0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001)
outcome ~ poisson −0.238*** −0.287*** −0.152*** −0.238*** −0.288*** −0.152*** −0.238*** −0.288*** −0.152*** −0.238*** −0.288*** −0.152***
(0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001)
outcome ~ probit −0.035*** −0.027*** −0.024*** −0.035*** −0.027*** −0.024*** −0.035*** −0.027*** −0.024*** −0.035*** −0.027*** −0.024***
(0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001) (0.002) (0.003) (0.001)
Num.Obs. 38212 38201 38242 38212 38201 38242 38212 38201 38242 38212 38201 38242
R2 0.344 0.317 0.364 0.349 0.327 0.364 0.349 0.328 0.364 0.354 0.338 0.364
R2 Adj. 0.344 0.317 0.364 0.349 0.327 0.364 0.349 0.328 0.364 0.354 0.337 0.364
AIC −30964.8 −4668.4 −79374.9 −31245.9 −5213.3 −79387.9 −31227.3 −5271.8 −79373.2 −31513.9 −5834.6 −79386.3
BIC −30870.8 −4574.3 −79280.9 −31134.7 −5102.1 −79276.8 −31124.7 −5169.2 −79270.6 −31394.2 −5714.9 −79266.5
Log.Lik. 15493.423 2345.177 39698.473 15635.955 2619.649 39706.974 15625.654 2647.885 39698.624 15770.956 2931.290 39707.130
RMSE 0.16 0.23 0.09 0.16 0.23 0.09 0.16 0.23 0.09 0.16 0.22 0.09

betaS0 : intercept in selection equation

Main Effects 2nd Order Effects Interaction Effects Both Effects
DV : Absolute Error of betaS0, sample trimmed off 0.3%
Heckit Copula Heckit Copula Heckit Copula Heckit Copula
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept) 0.300*** 0.090*** 0.201*** 0.080*** 0.300*** 0.090*** 0.201*** 0.080***
(0.002) (0.001) (0.003) (0.001) (0.002) (0.001) (0.003) (0.001)
dependence −0.001 −0.001 0.011 0.012** −0.001 −0.001 0.011 0.012**
(0.003) (0.001) (0.009) (0.004) (0.003) (0.001) (0.009) (0.004)
dependence^2 −0.015 −0.016** −0.015 −0.016**
(0.011) (0.005) (0.011) (0.005)
selectivity −0.051*** −0.004*** −0.051*** −0.004*** −0.052*** −0.004*** −0.052*** −0.004***
(0.001) (0.000) (0.001) (0.000) (0.002) (0.001) (0.001) (0.001)
selectivity^2 0.147*** 0.014*** 0.147*** 0.014***
(0.002) (0.001) (0.002) (0.001)
dependence*selectivity 0.002 0.001 0.002 0.001
(0.003) (0.001) (0.003) (0.001)
X1 ~ normal - - - - - - - -
X1 ~ uniform −0.005* −0.005*** −0.005* −0.005*** −0.005* −0.005*** −0.005* −0.005***
(0.002) (0.001) (0.002) (0.001) (0.002) (0.001) (0.002) (0.001)
X1 ~ poisson 0.081*** 0.030*** 0.082*** 0.030*** 0.081*** 0.030*** 0.082*** 0.030***
(0.002) (0.001) (0.002) (0.001) (0.002) (0.001) (0.002) (0.001)
X1 ~ normal mixture 0.011*** 0.008*** 0.011*** 0.008*** 0.011*** 0.008*** 0.011*** 0.008***
(0.002) (0.001) (0.002) (0.001) (0.002) (0.001) (0.002) (0.001)
selection ~ logit - - - - - - - -
selection ~ probit −0.242*** −0.022*** −0.242*** −0.022*** −0.242*** −0.022*** −0.242*** −0.022***
(0.002) (0.001) (0.001) (0.001) (0.002) (0.001) (0.001) (0.001)
outcome ~ logit - - - - - - - -
outcome ~ normal 0.000 −0.001 0.000 −0.001 0.000 −0.001 0.000 −0.001
(0.002) (0.001) (0.002) (0.001) (0.002) (0.001) (0.002) (0.001)
outcome ~ poisson 0.000 −0.001 0.000 −0.001 0.000 −0.001 0.000 −0.001
(0.002) (0.001) (0.002) (0.001) (0.002) (0.001) (0.002) (0.001)
outcome ~ probit 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
(0.002) (0.001) (0.002) (0.001) (0.002) (0.001) (0.002) (0.001)
Num.Obs. 38284 38286 38284 38286 38284 38286 38284 38286
R2 0.415 0.065 0.530 0.075 0.415 0.065 0.530 0.075
R2 Adj. 0.415 0.065 0.530 0.074 0.415 0.065 0.530 0.074
AIC −33258.7 −98415.8 −41610.4 −98797.1 −33257.3 −98414.0 −41609.1 −98795.3
BIC −33164.6 −98321.7 −41499.2 −98685.9 −33154.7 −98311.4 −41489.4 −98675.6
Log.Lik. 16640.347 49218.902 20818.215 49411.552 16640.643 49219.004 20818.561 49411.656
RMSE 0.16 0.07 0.14 0.07 0.16 0.07 0.14 0.07

betaS1 : coefficient on endogenous variable X1

Main Effects 2nd Order Effects Interaction Effects Both Effects
DV : Absolute Error of betaS1, sample trimmed off 0.3%
Heckit Copula Heckit Copula Heckit Copula Heckit Copula
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept) 0.403*** 0.095*** 0.397*** 0.092*** 0.403*** 0.095*** 0.397*** 0.092***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
dependence 0.005*** 0.002+ 0.009* 0.008* 0.005*** 0.002+ 0.009* 0.008*
(0.001) (0.001) (0.004) (0.004) (0.001) (0.001) (0.004) (0.004)
dependence^2 −0.005 −0.008 −0.005 −0.008
(0.005) (0.005) (0.005) (0.005)
selectivity 0.003*** 0.000 0.003*** 0.000 0.002* −0.002*** 0.002* −0.002***
(0.000) (0.000) (0.000) (0.000) (0.001) (0.001) (0.001) (0.001)
selectivity^2 0.010*** 0.004*** 0.010*** 0.004***
(0.001) (0.001) (0.001) (0.001)
dependence*selectivity 0.003* 0.007*** 0.003* 0.007***
(0.001) (0.001) (0.001) (0.001)
X1 ~ normal - - - - - - - -
X1 ~ uniform 0.008*** 0.026*** 0.008*** 0.026*** 0.008*** 0.026*** 0.008*** 0.026***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
X1 ~ poisson −0.002 −0.002+ −0.002 −0.002+ −0.002 −0.002+ −0.002 −0.002+
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
X1 ~ normal mixture 0.003** −0.012*** 0.003** −0.012*** 0.003** −0.012*** 0.003** −0.012***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
selection ~ logit - - - - - - - -
selection ~ probit −0.325*** −0.020*** −0.325*** −0.020*** −0.325*** −0.020*** −0.325*** −0.020***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
outcome ~ logit - - - - - - - -
outcome ~ normal 0.000 −0.001 0.000 −0.001 0.000 −0.001 0.000 −0.001
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
outcome ~ poisson 0.000 −0.002* 0.000 −0.002* 0.000 −0.002* 0.000 −0.002*
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
outcome ~ probit 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
Num.Obs. 38267 38271 38267 38271 38267 38271 38267 38271
R2 0.842 0.059 0.843 0.059 0.842 0.059 0.843 0.060
R2 Adj. 0.842 0.059 0.843 0.059 0.842 0.059 0.843 0.060
AIC −94405.3 −97367.0 −94557.4 −97389.3 −94408.1 −97391.8 −94560.2 −97414.2
BIC −94311.2 −97272.9 −94446.2 −97278.1 −94305.5 −97289.2 −94440.5 −97294.5
Log.Lik. 47213.640 48694.477 47291.691 48707.661 47216.058 48707.901 47294.114 48721.098
RMSE 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07

betaS2 : coefficient on exogenous variable X2

Main Effects 2nd Order Effects Interaction Effects Both Effects
DV : Absolute Error of betaS2, sample trimmed off 0.3%
Heckit Copula Heckit Copula Heckit Copula Heckit Copula
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept) 0.053*** 0.088*** 0.052*** 0.086*** 0.053*** 0.088*** 0.052*** 0.086***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
dependence 0.001* −0.001 −0.010*** −0.009** 0.001* −0.001 −0.010*** −0.009**
(0.001) (0.001) (0.003) (0.003) (0.001) (0.001) (0.003) (0.003)
dependence^2 0.015*** 0.011** 0.015*** 0.011**
(0.003) (0.004) (0.003) (0.004)
selectivity −0.001*** −0.001*** −0.001*** −0.001*** −0.001*** −0.002** −0.001*** −0.002**
(0.000) (0.000) (0.000) (0.000) (0.000) (0.001) (0.000) (0.001)
selectivity^2 0.003*** 0.003*** 0.003*** 0.003***
(0.000) (0.001) (0.000) (0.001)
dependence*selectivity 0.001 0.001 0.001 0.001
(0.001) (0.001) (0.001) (0.001)
X1 ~ normal - - - - - - - -
X1 ~ uniform −0.005*** −0.006*** −0.005*** −0.006*** −0.005*** −0.006*** −0.005*** −0.006***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
X1 ~ poisson −0.003*** −0.004*** −0.003*** −0.004*** −0.003*** −0.004*** −0.003*** −0.004***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
X1 ~ normal mixture 0.004*** 0.006*** 0.004*** 0.006*** 0.004*** 0.006*** 0.004*** 0.006***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
selection ~ logit - - - - - - - -
selection ~ probit 0.007*** −0.027*** 0.007*** −0.027*** 0.007*** −0.027*** 0.007*** −0.027***
(0.000) (0.001) (0.000) (0.001) (0.000) (0.001) (0.000) (0.001)
outcome ~ logit - - - - - - - -
outcome ~ normal 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
outcome ~ poisson 0.000 −0.002* 0.000 −0.002* 0.000 −0.002* 0.000 −0.002*
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
outcome ~ probit 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
Num.Obs. 38300 38296 38300 38296 38300 38296 38300 38296
R2 0.015 0.063 0.016 0.064 0.015 0.063 0.016 0.064
R2 Adj. 0.014 0.063 0.016 0.064 0.014 0.063 0.016 0.064
AIC −134146.7 −113532.8 −134214.4 −113568.3 −134145.9 −113531.4 −134213.5 −113566.9
BIC −134052.7 −113438.7 −134103.2 −113457.1 −134043.3 −113428.7 −134093.8 −113447.1
Log.Lik. 67084.375 56777.401 67120.203 56797.133 67084.946 56777.694 67120.774 56797.426
RMSE 0.04 0.05 0.04 0.05 0.04 0.05 0.04 0.05

betaS3 : coefficient on exclusion restriction variable X3

Main Effects 2nd Order Effects Interaction Effects Both Effects
DV : Absolute Error of betaS3, sample trimmed off 0.3%
Heckit Copula Heckit Copula Heckit Copula Heckit Copula
+ p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001
(Intercept) 0.403*** 0.106*** 0.397*** 0.102*** 0.403*** 0.106*** 0.397*** 0.102***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
dependence 0.001 −0.005*** −0.002 0.010* 0.001 −0.005*** −0.002 0.010*
(0.001) (0.001) (0.005) (0.004) (0.001) (0.001) (0.005) (0.004)
dependence^2 0.003 −0.018*** 0.003 −0.018***
(0.006) (0.005) (0.006) (0.005)
selectivity −0.003*** 0.000 −0.003*** 0.000 −0.003*** 0.001 −0.003*** 0.001
(0.000) (0.000) (0.000) (0.000) (0.001) (0.001) (0.001) (0.001)
selectivity^2 0.009*** 0.005*** 0.009*** 0.005***
(0.001) (0.001) (0.001) (0.001)
dependence*selectivity 0.000 −0.003+ 0.000 −0.003+
(0.002) (0.001) (0.002) (0.001)
X1 ~ normal - - - - - - - -
X1 ~ uniform −0.010*** −0.005*** −0.010*** −0.005*** −0.010*** −0.005*** −0.010*** −0.005***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
X1 ~ poisson −0.004*** −0.002+ −0.004*** −0.002+ −0.004*** −0.002+ −0.004*** −0.002+
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
X1 ~ normal mixture 0.010*** 0.004*** 0.010*** 0.004*** 0.010*** 0.004*** 0.010*** 0.004***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
selection ~ logit - - - - - - - -
selection ~ probit −0.315*** −0.021*** −0.315*** −0.021*** −0.315*** −0.021*** −0.315*** −0.021***
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
outcome ~ logit - - - - - - - -
outcome ~ normal 0.000 −0.002 0.000 −0.002 0.000 −0.002 0.000 −0.002
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
outcome ~ poisson 0.000 −0.003** 0.000 −0.003** 0.000 −0.003** 0.000 −0.003**
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
outcome ~ probit 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000
(0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001) (0.001)
Num.Obs. 38287 38277 38287 38277 38287 38277 38287 38277
R2 0.818 0.025 0.819 0.026 0.818 0.025 0.819 0.026
R2 Adj. 0.818 0.025 0.819 0.026 0.818 0.025 0.819 0.026
AIC −90246.9 −93460.1 −90359.2 −93508.3 −90244.9 −93461.2 −90357.2 −93509.4
BIC −90152.8 −93366.0 −90248.0 −93397.1 −90142.2 −93358.6 −90237.4 −93389.7
Log.Lik. 45134.428 46741.035 45192.579 46767.129 45134.437 46742.610 45192.588 46768.700
RMSE 0.07 0.07 0.07 0.07 0.07 0.07 0.07 0.07

ANOVA & Interaction Plots

betaO0 : intercept in outcome equation

ANOVA : Logit - Logit Specification
Sum Sq Df F value Pr(>F)
(Intercept) 58.62 1 213.02 0.00
dependence 174.89 1 635.55 0.00
selectivity 4.08 1 14.82 0.00
x_dist 20.75 3 25.13 0.00
dependence:selectivity 25.53 1 92.78 0.00
dependence:x_dist 14.69 3 17.79 0.00
selectivity:x_dist 2.41 3 2.92 0.03
dependence:selectivity:x_dist 0.24 3 0.30 0.83
Residuals 3923.63 14258 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14258) = 213.02, p < .001; Eta2 (partial) = 0.04, 95% CI [0.04, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14258) = 635.55, p < .001; Eta2 (partial) = 1.04e-03, 95% CI [3.41e-04, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14258) = 14.82, p < .001; Eta2 (partial) = 5.26e-03, 95% CI [3.33e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14258) = 25.13, p < .001; Eta2 (partial) = 6.46e-03, 95% CI [4.45e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14258) = 92.78, p < .001; Eta2 (partial) = 3.73e-03, 95% CI [2.12e-03, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14258) = 17.79, p < .001; Eta2 (partial) = 6.15e-04, 95% CI [2.65e-05, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14258) = 2.92, p = 0.033; Eta2 (partial) = 6.24e-05, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14258) = 0.30, p = 0.828; Eta2 (partial) = 0.04, 95% CI [0.04, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Logit - Normal Specification
Sum Sq Df F value Pr(>F)
(Intercept) 12.63 1 431.10 0.00
dependence 13.90 1 474.47 0.00
selectivity 1.16 1 39.76 0.00
x_dist 1.95 3 22.22 0.00
dependence:selectivity 1.29 1 44.08 0.00
dependence:x_dist 1.31 3 14.95 0.00
selectivity:x_dist 0.03 3 0.35 0.79
dependence:selectivity:x_dist 0.09 3 0.98 0.40
Residuals 421.44 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 431.10, p < .001; Eta2 (partial) = 0.03, 95% CI [0.03, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 474.47, p < .001; Eta2 (partial) = 2.76e-03, 95% CI [1.51e-03, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14384) = 39.76, p < .001; Eta2 (partial) = 4.61e-03, 95% CI [2.82e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 22.22, p < .001; Eta2 (partial) = 3.06e-03, 95% CI [1.73e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14384) = 44.08, p < .001; Eta2 (partial) = 3.11e-03, 95% CI [1.65e-03, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14384) = 14.95, p < .001; Eta2 (partial) = 7.29e-05, 95% CI [0.00, 1.00])
  • The interaction between selectivity and x_dist is statistically not significant and very small (F(3, 14384) = 0.35, p = 0.789; Eta2 (partial) = 2.03e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14384) = 0.98, p = 0.403; Eta2 (partial) = 0.03, 95% CI [0.03, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Logit - Poisson Specification
Sum Sq Df F value Pr(>F)
(Intercept) 2.83 1 774.33 0
dependence 3.03 1 829.15 0
selectivity 0.19 1 52.39 0
x_dist 0.88 3 80.25 0
dependence:selectivity 0.27 1 74.38 0
dependence:x_dist 0.97 3 88.07 0
selectivity:x_dist 0.12 3 10.83 0
dependence:selectivity:x_dist 0.13 3 12.15 0
Residuals 52.61 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 774.33, p < .001; Eta2 (partial) = 0.05, 95% CI [0.05, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 829.15, p < .001; Eta2 (partial) = 3.63e-03, 95% CI [2.17e-03, 1.00])
  • The main effect of selectivity is statistically significant and small (F(1, 14384) = 52.39, p < .001; Eta2 (partial) = 0.02, 95% CI [0.01, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 80.25, p < .001; Eta2 (partial) = 5.14e-03, 95% CI [3.37e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and small (F(1, 14384) = 74.38, p < .001; Eta2 (partial) = 0.02, 95% CI [0.01, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14384) = 88.07, p < .001; Eta2 (partial) = 2.25e-03, 95% CI [1.02e-03, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14384) = 10.83, p < .001; Eta2 (partial) = 2.53e-03, 95% CI [1.22e-03, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically significant and small (F(3, 14384) = 12.15, p < .001; Eta2 (partial) = 0.05, 95% CI [0.05, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Logit - Probit Specification
Sum Sq Df F value Pr(>F)
(Intercept) 47.15 1 299.85 0.00
dependence 91.32 1 580.81 0.00
selectivity 4.66 1 29.67 0.00
x_dist 8.17 3 17.32 0.00
dependence:selectivity 11.01 1 70.03 0.00
dependence:x_dist 10.60 3 22.48 0.00
selectivity:x_dist 1.73 3 3.67 0.01
dependence:selectivity:x_dist 0.42 3 0.90 0.44
Residuals 2242.14 14260 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14260) = 299.85, p < .001; Eta2 (partial) = 0.04, 95% CI [0.03, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14260) = 580.81, p < .001; Eta2 (partial) = 2.08e-03, 95% CI [1.01e-03, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14260) = 29.67, p < .001; Eta2 (partial) = 3.63e-03, 95% CI [2.04e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14260) = 17.32, p < .001; Eta2 (partial) = 4.89e-03, 95% CI [3.16e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14260) = 70.03, p < .001; Eta2 (partial) = 4.71e-03, 95% CI [2.89e-03, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14260) = 22.48, p < .001; Eta2 (partial) = 7.71e-04, 95% CI [9.60e-05, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14260) = 3.67, p = 0.012; Eta2 (partial) = 1.89e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14260) = 0.90, p = 0.441; Eta2 (partial) = 0.04, 95% CI [0.03, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Probit - Logit Specification
Sum Sq Df F value Pr(>F)
(Intercept) 51.90 1 275.86 0.00
dependence 89.80 1 477.35 0.00
selectivity 4.97 1 26.42 0.00
x_dist 19.73 3 34.96 0.00
dependence:selectivity 23.38 1 124.28 0.00
dependence:x_dist 12.12 3 21.47 0.00
selectivity:x_dist 3.30 3 5.85 0.00
dependence:selectivity:x_dist 0.08 3 0.15 0.93
Residuals 2691.60 14307 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14307) = 275.86, p < .001; Eta2 (partial) = 0.03, 95% CI [0.03, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14307) = 477.35, p < .001; Eta2 (partial) = 1.84e-03, 95% CI [8.53e-04, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14307) = 26.42, p < .001; Eta2 (partial) = 7.28e-03, 95% CI [5.01e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14307) = 34.96, p < .001; Eta2 (partial) = 8.61e-03, 95% CI [6.27e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14307) = 124.28, p < .001; Eta2 (partial) = 4.48e-03, 95% CI [2.71e-03, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14307) = 21.47, p < .001; Eta2 (partial) = 1.22e-03, 95% CI [3.43e-04, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14307) = 5.85, p < .001; Eta2 (partial) = 3.11e-05, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14307) = 0.15, p = 0.931; Eta2 (partial) = 0.03, 95% CI [0.03, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Probit - Normal Specification
Sum Sq Df F value Pr(>F)
(Intercept) 8.79 1 381.22 0.00
dependence 9.86 1 427.66 0.00
selectivity 1.03 1 44.66 0.00
x_dist 1.84 3 26.65 0.00
dependence:selectivity 1.61 1 69.98 0.00
dependence:x_dist 1.42 3 20.57 0.00
selectivity:x_dist 0.10 3 1.46 0.22
dependence:selectivity:x_dist 0.33 3 4.80 0.00
Residuals 331.54 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 381.22, p < .001; Eta2 (partial) = 0.03, 95% CI [0.02, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 427.66, p < .001; Eta2 (partial) = 3.10e-03, 95% CI [1.76e-03, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14384) = 44.66, p < .001; Eta2 (partial) = 5.53e-03, 95% CI [3.56e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 26.65, p < .001; Eta2 (partial) = 4.84e-03, 95% CI [3.13e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14384) = 69.98, p < .001; Eta2 (partial) = 4.27e-03, 95% CI [2.55e-03, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14384) = 20.57, p < .001; Eta2 (partial) = 3.04e-04, 95% CI [0.00, 1.00])
  • The interaction between selectivity and x_dist is statistically not significant and very small (F(3, 14384) = 1.46, p = 0.224; Eta2 (partial) = 1.00e-03, 95% CI [2.17e-04, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically significant and small (F(3, 14384) = 4.80, p = 0.002; Eta2 (partial) = 0.03, 95% CI [0.02, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Probit - Poisson Specification
Sum Sq Df F value Pr(>F)
(Intercept) 2.06 1 790.24 0
dependence 1.86 1 712.91 0
selectivity 0.14 1 55.04 0
x_dist 0.65 3 82.83 0
dependence:selectivity 0.30 1 114.90 0
dependence:x_dist 0.90 3 115.54 0
selectivity:x_dist 0.13 3 16.96 0
dependence:selectivity:x_dist 0.20 3 25.83 0
Residuals 37.54 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 790.24, p < .001; Eta2 (partial) = 0.05, 95% CI [0.04, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 712.91, p < .001; Eta2 (partial) = 3.81e-03, 95% CI [2.31e-03, 1.00])
  • The main effect of selectivity is statistically significant and small (F(1, 14384) = 55.04, p < .001; Eta2 (partial) = 0.02, 95% CI [0.01, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 82.83, p < .001; Eta2 (partial) = 7.93e-03, 95% CI [5.69e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and small (F(1, 14384) = 114.90, p < .001; Eta2 (partial) = 0.02, 95% CI [0.02, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14384) = 115.54, p < .001; Eta2 (partial) = 3.53e-03, 95% CI [1.97e-03, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14384) = 16.96, p < .001; Eta2 (partial) = 5.36e-03, 95% CI [3.42e-03, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically significant and small (F(3, 14384) = 25.83, p < .001; Eta2 (partial) = 0.05, 95% CI [0.04, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

betaO1 : coefficient on endogenous variable X1

ANOVA : Logit - Logit Specification
Sum Sq Df F value Pr(>F)
(Intercept) 43.29 1 588.88 0.00
dependence 15.27 1 207.66 0.00
selectivity 1.18 1 16.04 0.00
x_dist 3.90 3 17.67 0.00
dependence:selectivity 3.03 1 41.29 0.00
dependence:x_dist 1.99 3 9.01 0.00
selectivity:x_dist 0.33 3 1.51 0.21
dependence:selectivity:x_dist 0.54 3 2.44 0.06
Residuals 1052.07 14312 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14312) = 588.88, p < .001; Eta2 (partial) = 0.01, 95% CI [0.01, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14312) = 207.66, p < .001; Eta2 (partial) = 1.12e-03, 95% CI [3.89e-04, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14312) = 16.04, p < .001; Eta2 (partial) = 3.69e-03, 95% CI [2.09e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14312) = 17.67, p < .001; Eta2 (partial) = 2.88e-03, 95% CI [1.59e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14312) = 41.29, p < .001; Eta2 (partial) = 1.89e-03, 95% CI [7.66e-04, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14312) = 9.01, p < .001; Eta2 (partial) = 3.16e-04, 95% CI [0.00, 1.00])
  • The interaction between selectivity and x_dist is statistically not significant and very small (F(3, 14312) = 1.51, p = 0.211; Eta2 (partial) = 5.12e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14312) = 2.44, p = 0.062; Eta2 (partial) = 0.01, 95% CI [0.01, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Logit - Normal Specification
Sum Sq Df F value Pr(>F)
(Intercept) 5.18 1 1235.87 0.00
dependence 1.02 1 244.33 0.00
selectivity 0.15 1 36.32 0.00
x_dist 2.68 3 213.04 0.00
dependence:selectivity 0.02 1 3.85 0.05
dependence:x_dist 0.01 3 1.18 0.32
selectivity:x_dist 0.14 3 11.33 0.00
dependence:selectivity:x_dist 0.01 3 0.56 0.64
Residuals 60.34 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 1235.87, p < .001; Eta2 (partial) = 0.02, 95% CI [0.01, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 244.33, p < .001; Eta2 (partial) = 2.52e-03, 95% CI [1.33e-03, 1.00])
  • The main effect of selectivity is statistically significant and small (F(1, 14384) = 36.32, p < .001; Eta2 (partial) = 0.04, 95% CI [0.04, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 213.04, p < .001; Eta2 (partial) = 2.68e-04, 95% CI [2.07e-07, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14384) = 3.85, p = 0.050; Eta2 (partial) = 2.46e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence and x_dist is statistically not significant and very small (F(3, 14384) = 1.18, p = 0.316; Eta2 (partial) = 2.36e-03, 95% CI [1.10e-03, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14384) = 11.33, p < .001; Eta2 (partial) = 1.17e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14384) = 0.56, p = 0.640; Eta2 (partial) = 0.02, 95% CI [0.01, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Logit - Poisson Specification
Sum Sq Df F value Pr(>F)
(Intercept) 0.57 1 677.56 0
dependence 0.49 1 587.57 0
selectivity 0.02 1 25.51 0
x_dist 1.48 3 589.02 0
dependence:selectivity 0.04 1 42.00 0
dependence:x_dist 0.61 3 243.77 0
selectivity:x_dist 0.04 3 14.91 0
dependence:selectivity:x_dist 0.08 3 31.43 0
Residuals 12.07 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 677.56, p < .001; Eta2 (partial) = 0.04, 95% CI [0.03, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 587.57, p < .001; Eta2 (partial) = 1.77e-03, 95% CI [8.06e-04, 1.00])
  • The main effect of selectivity is statistically significant and medium (F(1, 14384) = 25.51, p < .001; Eta2 (partial) = 0.11, 95% CI [0.10, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 589.02, p < .001; Eta2 (partial) = 2.91e-03, 95% CI [1.62e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and small (F(1, 14384) = 42.00, p < .001; Eta2 (partial) = 0.05, 95% CI [0.04, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14384) = 243.77, p < .001; Eta2 (partial) = 3.10e-03, 95% CI [1.64e-03, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14384) = 14.91, p < .001; Eta2 (partial) = 6.51e-03, 95% CI [4.37e-03, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically significant and small (F(3, 14384) = 31.43, p < .001; Eta2 (partial) = 0.04, 95% CI [0.03, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Logit - Probit Specification
Sum Sq Df F value Pr(>F)
(Intercept) 19.87 1 284.90 0.00
dependence 10.34 1 148.28 0.00
selectivity 0.19 1 2.66 0.10
x_dist 4.54 3 21.70 0.00
dependence:selectivity 3.34 1 47.89 0.00
dependence:x_dist 1.60 3 7.67 0.00
selectivity:x_dist 1.06 3 5.06 0.00
dependence:selectivity:x_dist 0.27 3 1.30 0.27
Residuals 993.22 14241 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14241) = 284.90, p < .001; Eta2 (partial) = 0.01, 95% CI [7.72e-03, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14241) = 148.28, p < .001; Eta2 (partial) = 1.87e-04, 95% CI [0.00, 1.00])
  • The main effect of selectivity is statistically not significant and very small (F(1, 14241) = 2.66, p = 0.103; Eta2 (partial) = 4.55e-03, 95% CI [2.76e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14241) = 21.70, p < .001; Eta2 (partial) = 3.35e-03, 95% CI [1.95e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14241) = 47.89, p < .001; Eta2 (partial) = 1.61e-03, 95% CI [5.83e-04, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14241) = 7.67, p < .001; Eta2 (partial) = 1.06e-03, 95% CI [2.48e-04, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14241) = 5.06, p = 0.002; Eta2 (partial) = 2.73e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14241) = 1.30, p = 0.273; Eta2 (partial) = 0.01, 95% CI [7.72e-03, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Probit - Logit Specification
Sum Sq Df F value Pr(>F)
(Intercept) 50.17 1 786.94 0.00
dependence 9.35 1 146.66 0.00
selectivity 2.68 1 42.00 0.00
x_dist 3.69 3 19.28 0.00
dependence:selectivity 2.32 1 36.45 0.00
dependence:x_dist 0.79 3 4.12 0.01
selectivity:x_dist 0.26 3 1.34 0.26
dependence:selectivity:x_dist 0.47 3 2.45 0.06
Residuals 911.69 14301 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14301) = 786.94, p < .001; Eta2 (partial) = 0.01, 95% CI [7.59e-03, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14301) = 146.66, p < .001; Eta2 (partial) = 2.93e-03, 95% CI [1.63e-03, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14301) = 42.00, p < .001; Eta2 (partial) = 4.03e-03, 95% CI [2.35e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14301) = 19.28, p < .001; Eta2 (partial) = 2.54e-03, 95% CI [1.35e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14301) = 36.45, p < .001; Eta2 (partial) = 8.63e-04, 95% CI [1.42e-04, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14301) = 4.12, p = 0.006; Eta2 (partial) = 2.81e-04, 95% CI [0.00, 1.00])
  • The interaction between selectivity and x_dist is statistically not significant and very small (F(3, 14301) = 1.34, p = 0.260; Eta2 (partial) = 5.13e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14301) = 2.45, p = 0.062; Eta2 (partial) = 0.01, 95% CI [7.59e-03, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Probit - Normal Specification
Sum Sq Df F value Pr(>F)
(Intercept) 5.21 1 1132.52 0.00
dependence 1.30 1 282.27 0.00
selectivity 0.14 1 30.85 0.00
x_dist 3.04 3 220.41 0.00
dependence:selectivity 0.08 1 18.09 0.00
dependence:x_dist 0.08 3 6.15 0.00
selectivity:x_dist 0.25 3 18.24 0.00
dependence:selectivity:x_dist 0.02 3 1.52 0.21
Residuals 66.23 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 1132.52, p < .001; Eta2 (partial) = 0.02, 95% CI [0.02, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 282.27, p < .001; Eta2 (partial) = 2.14e-03, 95% CI [1.06e-03, 1.00])
  • The main effect of selectivity is statistically significant and small (F(1, 14384) = 30.85, p < .001; Eta2 (partial) = 0.04, 95% CI [0.04, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 220.41, p < .001; Eta2 (partial) = 1.26e-03, 95% CI [4.73e-04, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14384) = 18.09, p < .001; Eta2 (partial) = 1.28e-03, 95% CI [3.79e-04, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14384) = 6.15, p < .001; Eta2 (partial) = 3.79e-03, 95% CI [2.17e-03, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14384) = 18.24, p < .001; Eta2 (partial) = 3.16e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14384) = 1.52, p = 0.208; Eta2 (partial) = 0.02, 95% CI [0.02, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Probit - Poisson Specification
Sum Sq Df F value Pr(>F)
(Intercept) 0.51 1 618.29 0
dependence 0.30 1 359.31 0
selectivity 0.02 1 24.22 0
x_dist 1.67 3 672.46 0
dependence:selectivity 0.03 1 38.86 0
dependence:x_dist 0.48 3 193.80 0
selectivity:x_dist 0.09 3 35.45 0
dependence:selectivity:x_dist 0.07 3 27.44 0
Residuals 11.89 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 618.29, p < .001; Eta2 (partial) = 0.02, 95% CI [0.02, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 359.31, p < .001; Eta2 (partial) = 1.68e-03, 95% CI [7.45e-04, 1.00])
  • The main effect of selectivity is statistically significant and medium (F(1, 14384) = 24.22, p < .001; Eta2 (partial) = 0.12, 95% CI [0.11, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 672.46, p < .001; Eta2 (partial) = 2.69e-03, 95% CI [1.46e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and small (F(1, 14384) = 38.86, p < .001; Eta2 (partial) = 0.04, 95% CI [0.03, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14384) = 193.80, p < .001; Eta2 (partial) = 7.34e-03, 95% CI [5.07e-03, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14384) = 35.45, p < .001; Eta2 (partial) = 5.69e-03, 95% CI [3.69e-03, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically significant and small (F(3, 14384) = 27.44, p < .001; Eta2 (partial) = 0.02, 95% CI [0.02, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

betaO2 : coefficient on exogenous variable X2

ANOVA : Logit - Logit Specification
Sum Sq Df F value Pr(>F)
(Intercept) 27.40 1 456.02 0.00
dependence 30.96 1 515.43 0.00
selectivity 0.79 1 13.08 0.00
x_dist 2.25 3 12.47 0.00
dependence:selectivity 2.80 1 46.67 0.00
dependence:x_dist 5.31 3 29.48 0.00
selectivity:x_dist 0.35 3 1.92 0.12
dependence:selectivity:x_dist 0.18 3 1.02 0.38
Residuals 857.93 14281 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14281) = 456.02, p < .001; Eta2 (partial) = 0.03, 95% CI [0.03, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14281) = 515.43, p < .001; Eta2 (partial) = 9.15e-04, 95% CI [2.72e-04, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14281) = 13.08, p < .001; Eta2 (partial) = 2.61e-03, 95% CI [1.28e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14281) = 12.47, p < .001; Eta2 (partial) = 3.26e-03, 95% CI [1.88e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14281) = 46.67, p < .001; Eta2 (partial) = 6.16e-03, 95% CI [4.07e-03, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14281) = 29.48, p < .001; Eta2 (partial) = 4.03e-04, 95% CI [0.00, 1.00])
  • The interaction between selectivity and x_dist is statistically not significant and very small (F(3, 14281) = 1.92, p = 0.124; Eta2 (partial) = 2.14e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14281) = 1.02, p = 0.384; Eta2 (partial) = 0.03, 95% CI [0.03, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Logit - Normal Specification
Sum Sq Df F value Pr(>F)
(Intercept) 3.89 1 2549.61 0.00
dependence 0.01 1 3.40 0.07
selectivity 0.07 1 43.74 0.00
x_dist 0.04 3 8.44 0.00
dependence:selectivity 0.00 1 2.44 0.12
dependence:x_dist 0.01 3 1.44 0.23
selectivity:x_dist 0.01 3 2.31 0.07
dependence:selectivity:x_dist 0.01 3 2.58 0.05
Residuals 21.93 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and very small (F(1, 14384) = 2549.61, p < .001; Eta2 (partial) = 2.36e-04, 95% CI [0.00, 1.00])
  • The main effect of dependence is statistically not significant and very small (F(1, 14384) = 3.40, p = 0.065; Eta2 (partial) = 3.03e-03, 95% CI [1.71e-03, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14384) = 43.74, p < .001; Eta2 (partial) = 1.76e-03, 95% CI [6.82e-04, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 8.44, p < .001; Eta2 (partial) = 1.70e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence and selectivity is statistically not significant and very small (F(1, 14384) = 2.44, p = 0.118; Eta2 (partial) = 2.99e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence and x_dist is statistically not significant and very small (F(3, 14384) = 1.44, p = 0.230; Eta2 (partial) = 4.81e-04, 95% CI [0.00, 1.00])
  • The interaction between selectivity and x_dist is statistically not significant and very small (F(3, 14384) = 2.31, p = 0.074; Eta2 (partial) = 5.37e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and very small (F(3, 14384) = 2.58, p = 0.052; Eta2 (partial) = 2.36e-04, 95% CI [0.00, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Logit - Poisson Specification
Sum Sq Df F value Pr(>F)
(Intercept) 0.39 1 1291.62 0
dependence 0.24 1 773.08 0
selectivity 0.00 1 14.72 0
x_dist 0.22 3 237.07 0
dependence:selectivity 0.04 1 125.33 0
dependence:x_dist 0.21 3 230.99 0
selectivity:x_dist 0.02 3 18.84 0
dependence:selectivity:x_dist 0.03 3 32.09 0
Residuals 4.39 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 1291.62, p < .001; Eta2 (partial) = 0.05, 95% CI [0.05, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 773.08, p < .001; Eta2 (partial) = 1.02e-03, 95% CI [3.34e-04, 1.00])
  • The main effect of selectivity is statistically significant and small (F(1, 14384) = 14.72, p < .001; Eta2 (partial) = 0.05, 95% CI [0.04, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 237.07, p < .001; Eta2 (partial) = 8.64e-03, 95% CI [6.30e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and small (F(1, 14384) = 125.33, p < .001; Eta2 (partial) = 0.05, 95% CI [0.04, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14384) = 230.99, p < .001; Eta2 (partial) = 3.91e-03, 95% CI [2.27e-03, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14384) = 18.84, p < .001; Eta2 (partial) = 6.65e-03, 95% CI [4.49e-03, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically significant and small (F(3, 14384) = 32.09, p < .001; Eta2 (partial) = 0.05, 95% CI [0.05, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Logit - Probit Specification
Sum Sq Df F value Pr(>F)
(Intercept) 15.53 1 282.91 0.00
dependence 24.60 1 447.99 0.00
selectivity 0.38 1 6.89 0.01
x_dist 3.47 3 21.06 0.00
dependence:selectivity 3.10 1 56.53 0.00
dependence:x_dist 1.31 3 7.94 0.00
selectivity:x_dist 0.83 3 5.06 0.00
dependence:selectivity:x_dist 0.24 3 1.46 0.22
Residuals 782.15 14244 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14244) = 282.91, p < .001; Eta2 (partial) = 0.03, 95% CI [0.03, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14244) = 447.99, p < .001; Eta2 (partial) = 4.84e-04, 95% CI [6.73e-05, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14244) = 6.89, p = 0.009; Eta2 (partial) = 4.42e-03, 95% CI [2.66e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14244) = 21.06, p < .001; Eta2 (partial) = 3.95e-03, 95% CI [2.41e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14244) = 56.53, p < .001; Eta2 (partial) = 1.67e-03, 95% CI [6.20e-04, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14244) = 7.94, p < .001; Eta2 (partial) = 1.07e-03, 95% CI [2.49e-04, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14244) = 5.06, p = 0.002; Eta2 (partial) = 3.08e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14244) = 1.46, p = 0.222; Eta2 (partial) = 0.03, 95% CI [0.03, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Probit - Logit Specification
Sum Sq Df F value Pr(>F)
(Intercept) 38.15 1 768.67 0.00
dependence 10.71 1 215.88 0.00
selectivity 2.06 1 41.58 0.00
x_dist 2.46 3 16.50 0.00
dependence:selectivity 2.07 1 41.76 0.00
dependence:x_dist 2.03 3 13.65 0.00
selectivity:x_dist 0.70 3 4.70 0.00
dependence:selectivity:x_dist 0.26 3 1.72 0.16
Residuals 708.79 14282 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14282) = 768.67, p < .001; Eta2 (partial) = 0.01, 95% CI [0.01, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14282) = 215.88, p < .001; Eta2 (partial) = 2.90e-03, 95% CI [1.61e-03, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14282) = 41.58, p < .001; Eta2 (partial) = 3.45e-03, 95% CI [1.91e-03, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14282) = 16.50, p < .001; Eta2 (partial) = 2.92e-03, 95% CI [1.62e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and very small (F(1, 14282) = 41.76, p < .001; Eta2 (partial) = 2.86e-03, 95% CI [1.46e-03, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14282) = 13.65, p < .001; Eta2 (partial) = 9.87e-04, 95% CI [2.07e-04, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14282) = 4.70, p = 0.003; Eta2 (partial) = 3.61e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and small (F(3, 14282) = 1.72, p = 0.161; Eta2 (partial) = 0.01, 95% CI [0.01, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Probit - Normal Specification
Sum Sq Df F value Pr(>F)
(Intercept) 4.11 1 2444.20 0.00
dependence 0.00 1 0.00 0.97
selectivity 0.21 1 123.07 0.00
x_dist 0.03 3 5.07 0.00
dependence:selectivity 0.00 1 0.30 0.59
dependence:x_dist 0.00 3 0.80 0.49
selectivity:x_dist 0.01 3 2.92 0.03
dependence:selectivity:x_dist 0.00 3 0.52 0.67
Residuals 24.19 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and very small (F(1, 14384) = 2444.20, p < .001; Eta2 (partial) = 8.63e-08, 95% CI [0.00, 1.00])
  • The main effect of dependence is statistically not significant and very small (F(1, 14384) = 1.24e-03, p = 0.972; Eta2 (partial) = 8.48e-03, 95% CI [6.16e-03, 1.00])
  • The main effect of selectivity is statistically significant and very small (F(1, 14384) = 123.07, p < .001; Eta2 (partial) = 1.06e-03, 95% CI [2.47e-04, 1.00])
  • The main effect of x_dist is statistically significant and very small (F(3, 14384) = 5.07, p = 0.002; Eta2 (partial) = 2.06e-05, 95% CI [0.00, 1.00])
  • The interaction between dependence and selectivity is statistically not significant and very small (F(1, 14384) = 0.30, p = 0.587; Eta2 (partial) = 1.67e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence and x_dist is statistically not significant and very small (F(3, 14384) = 0.80, p = 0.492; Eta2 (partial) = 6.09e-04, 95% CI [2.63e-05, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and very small (F(3, 14384) = 2.92, p = 0.033; Eta2 (partial) = 1.08e-04, 95% CI [0.00, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically not significant and very small (F(3, 14384) = 0.52, p = 0.670; Eta2 (partial) = 8.63e-08, 95% CI [0.00, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots

ANOVA : Probit - Poisson Specification
Sum Sq Df F value Pr(>F)
(Intercept) 0.38 1 1488.05 0.00
dependence 0.10 1 401.58 0.00
selectivity 0.00 1 5.71 0.02
x_dist 0.20 3 254.77 0.00
dependence:selectivity 0.04 1 149.69 0.00
dependence:x_dist 0.13 3 163.08 0.00
selectivity:x_dist 0.01 3 18.31 0.00
dependence:selectivity:x_dist 0.04 3 58.41 0.00
Residuals 3.69 14384 NA NA

The ANOVA suggests that:

  • The main effect of (Intercept) is statistically significant and small (F(1, 14384) = 1488.05, p < .001; Eta2 (partial) = 0.03, 95% CI [0.02, 1.00])
  • The main effect of dependence is statistically significant and very small (F(1, 14384) = 401.58, p < .001; Eta2 (partial) = 3.97e-04, 95% CI [3.76e-05, 1.00])
  • The main effect of selectivity is statistically significant and small (F(1, 14384) = 5.71, p = 0.017; Eta2 (partial) = 0.05, 95% CI [0.04, 1.00])
  • The main effect of x_dist is statistically significant and small (F(3, 14384) = 254.77, p < .001; Eta2 (partial) = 0.01, 95% CI [7.73e-03, 1.00])
  • The interaction between dependence and selectivity is statistically significant and small (F(1, 14384) = 149.69, p < .001; Eta2 (partial) = 0.03, 95% CI [0.03, 1.00])
  • The interaction between dependence and x_dist is statistically significant and very small (F(3, 14384) = 163.08, p < .001; Eta2 (partial) = 3.80e-03, 95% CI [2.18e-03, 1.00])
  • The interaction between selectivity and x_dist is statistically significant and small (F(3, 14384) = 18.31, p < .001; Eta2 (partial) = 0.01, 95% CI [9.12e-03, 1.00])
  • The interaction between dependence, selectivity and x_dist is statistically significant and small (F(3, 14384) = 58.41, p < .001; Eta2 (partial) = 0.03, 95% CI [0.02, 1.00])

Effect sizes were labelled following Field’s (2013) recommendations.

Two-way Interaction Plots